Please answer a,b,c,d. Thanks! 5.13 question has four choices. Assume that the s

Question

Please answer a,b,c,d. Thanks!

5.13 question has four choices. Assume that the student has no knowl- edge of the correct answers to any of the questions. She has de- cided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on A student is taking a multiple-choice exam in which each the ball will determine her answer to the question. There are five multiple-choice questions on the exam. Wh at is the probability that she will get a. five questions correct? b. at least four questions correct? c. no questions correct? d. no more than two questions correct?

Explanation / Answer

Binomial Probability = nCx * (p)x * (q)n-x, where n = number of trials and x is the number of successes.

Here n = 5, p = 1/4 = 0.25 and q = 1 - p = 0.75

(a) P(X = 5) = 5C5 * (0.25)5 * (q)5-5= 0.00098

(b) P( At lest 4) = P(X=4) + P(X = 5)

P(X=4) = 5C4 * (0.25)4 * (q)5-4= 0.01465

Therefore the required probability is = 0.00098 + 0.01465 = 0.01563

(c) P(X = 0) = 5C0 * (0.25)0 * (q)5-0= 0.2373

(d) P(No more than 2 question correct) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = 1) = 5C1 * (0.25)1 * (q)5-1= 0.3955

P(X = 2) = 5C2 * (0.25)2 * (q)5-2= 0.2637

Therefore P(X= 0) + P(X = 1) + P(X = 2) = 0.2373 + 0.3955 + 0.2637 = 0.8965

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